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Polynomial Division

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it is a project to teach people how to do a long division math involving polynomials.

it is a project to teach people how to do a long division math involving polynomials.

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  • 1. Dividing the same variable when you divide two terms with a common variable. You subtract the exponent of the division. Ex) x ³ x² = x³-² = x Ex) (2x³ + 4x² + 6x) 2x = 2x³ + 4x² + 6x 2x 2x 2x = 2x² + 2x + 3 Anything to the power of zero is always one
  • 2. Simplification and Reduction
    • Simplify: x ² + 9x + 14
    • x + 7
    • This kind a question can be done in either two ways: you can factor the quadratic and then cancel out the common factor, like this.
    • x² + 9x + 14
    • x + 7
    • = (x + 2) (x + 7)
    • x + 7
    • = x + 2
    • You can also solve for this problem by doing long division. Like this
    • x + 2
    • x + 7 x² + 9x + 14
    • - ( x² + 7x )
    • = 0 + 2x + 14
    • - ( 2x + 14 )
    • 0 + 0
    • In this case we have no reminder, so the answer is just x+ 2
  • 3. Long Division
    • 4x ² - 2x +3 quotient
    • X + 1 4x ³ + 2x² + x + 5 dividend
    • - (4x ³ + 4x² )
    • = 0 - 2x ² + x
    • - (-2x² - 2x)
    • 0 + 3x + 5
    • - (3x + 3)
    • = 2 this is called the remainder
    Divisor
  • 4. Dividing polynomial with “missing terms”
    • When dividing a polynomial with a missing term, you consider that missing term as a zero. It doesn’t matter if you put a negative sign or positive sign, it is the same.
    • ex) 8x ³ + 1
    • 2x+ 1
    • 4x² - 2x + 1
    • 2x + 1 8x³ + 0x² + 0x + 1
    • - (8x³ + 4x²)
    • = 0 -4x² + 0x
    • - ( -4x² - 2x)
    • = 0 + 2x + 1
    • - (2x + 1)
    • 0+ 0
    • In this question there is no remainder
  • 5. Expression for polynomial “A”
    • Ex) A ( x+ 1) – ( 2x + x + 14) = (3x – 2) (x + 4)
    • A (x + 1) = (3x – 2) (x+ 4) + (2x + x + 14)
    • = (3x ² + 12x -2x – 8)+ (2x + x+ 14)
    • A (x + 1) = (3x² + 13x + 6)
    • x + 1 (x + 1)
    • 3x + 10 R= -4
    • x + 1 3x² + 13x + 6
    • - (3x² + 3x)
    • = 0 + 10x + 6
    • - (10x + 10)
    • = - 4
  • 6. Problem solving
    • A B
    • D C
    • F E
    A1= 3x ² - 4x - 7 A2= 4x ² - 3x - 7 x + 1 x + 1 Find DE Find AB
  • 7. The diagram above
    • A1= 3x² - 4x – 7
    • A2= 4x² - 3x – 7
    • BC= x + 1
    • FE= x + 1
    • Find AF, DE, DC, and AB
    • To find AF you need to do a long division by using area one and FE
    • 3x – 7
    • x + 1 3x² - 4x – 7
    • - (3x² + 3x)
    • = -7x -7
    • + ( -7x – 7)
    • = o
    • so AF= 3x - 7
  • 8. The same diagram
    • AF= DE + BC
    • so since we have AF and BC we can find DE by subtracting AF by BC and that gives us DE
    • (3x – 7) – x - 1 = DE
    • DE= 2x – 8
    • To find DC you need to use area two divide by BC
    • 4x – 7
    • x + 1 4x² - 3x – 7
    • - (4x² + 4x)
    • = 0 -7x – 7
    • + (-7x – 7)
    • = 0
    • DC= 4x - 7
  • 9. The same diagram
    • now we have FE and DC and we are asked to find AB.
    • What you do is that you take FE + DC and that gives you AB
    • AB = 4x – 7 + x + 1
    • = 5x - 6
  • 10. Solving for a triangle by using Long Division
    • A= 14x ² + x – 3
    • B= 4x + 2
    • Find the Height
    • To solve for this kind a question you need to know that A= B * H
    • 2
    • So 2A= B* H
    • So now you substitute the numbers in
    • 2 ( 14x ² + x – 3) = (4x + 2) H
    • 28x² + 2x – 6 = (4x + 2) H
    • 28x² + 2x – 6 = H
    • 4x + 2
  • 11. the same triangle
    • Now to find the height you need to do long division, like this
    • 28x² + 2x – 6
    • 4x + 2
    • 7x – 3
    • 4x + 2 28x² + 2x – 6
    • - ( 28x² + 14x)
    • = 0 - 12x – 6
    • + (-12x – 6)
    • = 0
    • the height = 7x - 3
  • 12. Solving a Rectangle by using long division
    • Here are the given information
    • A= 8x ² + 22x + 15
    • H= 2x + 3
    • Find the base of this rectangle
    • So to find the base of a rectangle you need to know two things, and those two things are area and the Height.
    • So since we have given those two piece of information we can find out what the base is by doing long division.
    • 4x + 5
    • 2x + 3 8x ² + 22x + 15
    • - ( 8x ² + 12x)
    • = 10 + 15
    • - (10x + 15)
    • = 0 + 0

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